Cameras are commonly used to capture an image of a scene that includes one or more objects. Unfortunately, the images can be blurred. For example, a lens assembly used by the camera always includes lens aberrations that can cause noticeable blur in each image captured using that lens assembly under certain shooting conditions (e.g. certain f-number, focal length, etc).
Blur caused by lens aberrations is spatially variant (varies dependent on field position). However, it is possible to approximate the blur caused by lens aberrations locally using a spatially invariant convolution model as follows,B=K*L+N.  Equation(1).
In Equation (1) and elsewhere in this document, (i) “B” represents a blurry image, (ii) “L” represents a latent sharp image, (iii) “K” represents a point spread function (“PSF”) kernel, and (iv) “N” represents noise (including quantization errors, compression artifacts, etc.).
A non-blind PSF problem seeks to recover the PSF kernel K when the latent sharp image L is known.
One common approach to solving a PSF estimation problem includes reformulating it as an optimization problem in which a suitable cost function is minimized. A common cost function can consist of (i) one or more fidelity terms, which make the minimum conform to equation (1) modeling of the blurring process, and (ii) one or more regularization terms, which make the solution more stable and help to enforce prior information about the solution, such as sparseness.
An example of such a PSF cost function isc(K)=∥L*K−B∥pp+γ∥D*K∥qq.  Equation (2)
In Equation (2), and elsewhere in this document, (i) c(K) is the Point Spread Function estimation cost function, (ii) D denotes a regularization operator, (iii) ∥L*K−B∥pp is a fidelity term that forces the solution to satisfy the blurring model in Equation (1) with a noise term that is small, (iv) ∥D*K∥qq is a regularization term that helps to infuse prior information about arrays that can be considered a PSF kernel, (v) γ is a regularization weight that is a selected constant that helps to achieve the proper balance between the fidelity and the regularization terms (vi) the subscript p denotes the norm or pseudo-norm for the fidelity term(s) that results from assuming a certain probabilistic prior distribution modeling, (vii) the superscript p denotes the power for the fidelity term(s), (viii) the subscript q denotes the norm for the regularization term(s) that results from assuming a certain probabilistic prior distribution modeling, and (ix) the superscript q denotes the power for the regularization term(s).
When the noise and/or noise derivatives (depending on whether or not there are derivatives in the fidelity term) are assumed to follow a Gaussian distribution, the power p for the fidelity term(s) is equal to two (p=2); and when the image derivatives are assumed to follow a Gaussian distribution, the power q for the regularization term(s) is equal to two (q=2). This can be referred to as a “Gaussian prior”. It should be noted that p=2 is the most common choice and the corresponding cost function is then referred to as a regularized least squares cost function.
Alternatively, when the noise and/or noise derivatives are assumed to follow a Laplacian distribution, the power p for the fidelity term(s) is equal to one (p=1); and when the image derivatives are assumed to follow a Laplacian distribution, the power q for the regularization term(s) is equal to one (q=1). This can be referred to as a “Laplacian prior”.
Still alternatively, when the noise and/or noise derivatives are assumed to follow a hyper-Laplacian distribution, the power p for the fidelity term(s) is less than one (p<1); and when the image derivatives are assumed to follow a hyper-Laplacian distribution, the power q for the regularization term(s) is less than one (q<1). This can be referred to as a “hyper-Laplacian prior”.
For the example, if a 2-norm is used in the fidelity and regularization terms of Equation (2) (i.e., p=2), then a non-exclusive example of a closed form formula for the cost function of Equation 2 minimum is as follows:
                              F          ⁡                      (            K            )                          ≈                                                                              F                  ⁡                                      (                    L                    )                                                  _                            ⁢                              F                ⁡                                  (                  B                  )                                                                                                                          F                    ⁡                                          (                      L                      )                                                        _                                ⁢                                  F                  ⁡                                      (                    L                    )                                                              +                              γ                ⁢                                                                  ⁢                                                      F                    ⁡                                          (                      D                      )                                                        _                                ⁢                                  F                  ⁡                                      (                    D                    )                                                                                .                                    Equation        ⁢                                  ⁢                  (          3          )                    
In Equations (2) and (3), the regularization term is necessary to compensate for zero and near-zero values in F(L).
Unfortunately, existing methods for estimating the optics blur of a lens assembly of a camera are not entirely adequate and may not produce sufficiently accurate optics point spread functions (“PSFs”).